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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.07957 |
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| _version_ | 1866913729861386240 |
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| author | Inoue, Takuya |
| author_facet | Inoue, Takuya |
| contents | In this paper, we consider plane partitions $\text{PP}(λ; m)$ of a given shape $λ$, with entries at most $m$. We prove that the distributions of two statistics on $\text{PP}(λ; m)$ coincide: one is the number of rows containing $0$ and the other is the number of rows containing $m$. We also provide a bijective proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On refined enumerations of plane partitions of a given shape with bounded entries Inoue, Takuya Combinatorics In this paper, we consider plane partitions $\text{PP}(λ; m)$ of a given shape $λ$, with entries at most $m$. We prove that the distributions of two statistics on $\text{PP}(λ; m)$ coincide: one is the number of rows containing $0$ and the other is the number of rows containing $m$. We also provide a bijective proof. |
| title | On refined enumerations of plane partitions of a given shape with bounded entries |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.07957 |